Is there something similar to curves' tilt for skin modifier?
From the very nature of the Skin modifier, this is not possible. Vertices do not have any rotational data, only location data. Because of this, it would be impossible to "tilt" the Skin modifier result, as it uses vertices to interpolate the resulting mesh.

Most of the examples I have seen the modeller is using curves. By using extrusion and bevel you can make great flat laces, and round ones are even easier. They also are completely editable at all times. 

I would strongly recommend using curves for this.

There is one example here that you can see. There is also a solution for one of the issues you might run into.